Entropy balance for mixtures

Putting this into the energy equation (3.81), taking into account the following, 

The entropy flow is based on a heat or material flow, the entropy generation on a heat flow in a temperature field, diffusion by mass forces and differences in the chemical potential, mechanical dissipation and chemical reactions. 

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Likewise (3.81) presupposes vanishing bulk viscosity. The derivation of the entropy balance for mixtures can be found in Appendix A 5. 

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